Numerous sources indicate that one must, indeed, live near his parents. The Gemara states that Yaakov Avinu (a”h) was punished for the years he spent away from his parents, clearly implying that one must live near his parents so he can fulfill the Mitzvah of Kibud Av Va’em. The Maharil of Germany (a”h), as cited in his “Likkutim,” stated explicitly that a person should live near his parents. The Rambam (a”h) comments that if a person’s parents became senile, then the son should move somewhere else – implying that under normal circumstances one should live near his parents.
Furthermore, Reb Yehudah Ha’Chasid (a”h) states in his Sefer Ha’Chasidim that if one’s parents instruct him not to get married, because they are afraid that he would then move away, he should not listen to them; rather, he should get married and live with or near his parents. Once again, we see that if the parents want their child to live near them, then he should accede to their wishes. The Aruch Ha’shulchan states that a person does not have to adhere to his parents’ demand that he not go away from town to learn Torah. The Gemara does inform us that Yaakov was not punished for the years he spent away from home learning in the Yeshiva of Shem and Ever, thus demonstrating that one may leave his parents’ city – even against their wishes – for the purpose of learning Torah.
There are however, several important exceptions to this law. The Aruch Ha’shulchan concludes that if one needs to move away for purposes of earning a living – where his job requires him to relocate – then he may move away even against his parents’ wishes. Furthermore, if living near one’s parents may threaten his Shalom Bayit, then he may move away. Certainly, if there are no suitable options for one’s children’s Jewish education in the area where his parents live, then he may move elsewhere for the sake of his children’s education. And, it goes without saying that if the parents approve of their child’s decision to move away, then he is permitted to do so.